To this must be added, that when | number of places, is no guarantee for we know the causes, we may be able its existence in any other place, since to judge whether there exists any there is no uniformity in the colloknown cause capable of counteracting cations of primeval causes. When, them; while as long as they are un- therefore, an empirical law is exknown, we cannot be sure but that if tended beyond the local limits within we did know them, we could predict which it has been found true by obtheir destruction from causes actually servation, the cases to which it is thus in existence. A bedridden savage, extended must be such as are presumwho had never seen the cataract of ably within the influence of the same Niagara, but who lived within hearing individual agents. If we discover a of it, might imagine that the sound new planet within the known bounds he heard would endure for ever; but of the solar system, (or even beyond if he knew it to be the effect of a rush those bounds, but indicating its conof waters over a barrier of rock which nection with the system by revolving is progressively wearing away, he round the sun,) we may conclude, would know that within a number of with great probability, that it revolves ages which may be calculated it will on its axis. For all the known planets be heard no more. In proportion, do so; and this uniformity points to therefore, to our ignorance of the some common cause antecedent to causes on which the empirical law the first records of astronomical obdepends, we can be less assured that servation: and though the nature of it will continue to hold good; and this cause can only be matter of conthe farther we look into futurity, the jecture, yet if it be, as is not unlikely, less improbable is it that some one of and as Laplace's theory supposes, not the causes whose co-existence gives merely the same kind of cause, but rise to the derivative uniformity may the same individual cause, (such as an be destroyed or counteracted, With impulse given to all the bodies at every prolongation of time the chances once,) that cause, acting at the exmultiply of such an event, that is to treme points of the space occupied by say, its non-occurrence hitherto be- the sun and planets, is likely, unless comes a less guarantee of its not defeated by some counteracting cause, occurring within the given time. If, to have acted at every intermediate then, it is only to cases which in point point, and probably somewhat beyond; of time are adjacent (or nearly adja- and therefore acted, in all probability, cent) to those which we have actually upon the supposed newly-discovered observed that any derivative law, not planet. of causation, can be extended with an assurance equivalent to certainty, much more is this true of a merely empirical law. Happily, for the purposes of life it is to such cases alone that we can almost ever have occasion to extend them.

In respect of place, it might seem that a merely empirical law could not be extended even to adjacent cases; that we could have no assurance of its being true in any place where it has not been specially observed. The past duration of a cause is a guarantee for its future existence, unless something occurs to destroy it; but the existence of a cause in one or any

When, therefore, effects which are always found conjoined can be traced with any probability to an identical (and not merely a similar) origin, we may with the same probability extend the empirical law of their conjunction to all places within the extreme local boundaries within which the fact has been observed; subject to the possibility of counteracting causes in some portion of the field. Still more confidently may we do so when the law is not merely empirical.; when the phenomena which we find conjoined are effects of ascertained causes, from the laws of which the conjunction of their effects is deducible. In that

case, we may both extend the derivative uniformity over a larger space, and with less abatement for the chance of counteracting causes. The first, because, instead of the local boundaries of our observation of the fact itself, we may include the extreme boundaries of the ascertained influence of its causes. Thus the succession of day and night, we know, holds true of all the bodies of the solar system except the sun itself; but we know this only because we are acquainted with the causes: if we were not, we could not extend the proposition beyond the orbits of the earth and moon, at both extremities of which we have the evidence of observation for its truth. With respect to the probability of counteracting causes, it has been seen that this calls for a greater abatement of confidence, in proportion to our ignorance of the causes on which the phenomena depend. On both accounts, therefore, a derivative law which we know how to resolve is susceptible of a greater extension to cases adjacent in place than a merely empirical law.

CHAPTER XX.

OF ANALOGY.

country, the expression is analogical, signifying that the colonies of a country stand in the same relation to her in which children stand to their parents. And if any inference be drawn from this resemblance of relations, as, for instance, that obedience or affection is due from colonies to the mother country, this is called reasoning by analogy. Or if it be argued that a nation is most beneficially governed by an assembly elected by the people, from the admitted fact that other associations for a common purpose, such as jointstock companies, are best managed by a committee chosen by the parties interested; this, too, is an argument from analogy in the preceding sense, because its foundation is, not that a nation is like a joint-stock company, or Parliament like a board of directors, but that Parliament stands in the same relation to the nation in which a board of directors stands to a joint-stock company. Now, in an argument of this nature, there is no inherent inferiority of conclusiveness. Like other arguments from resemblance, it may amount to nothing, or it may be a perfect and conclusive induction. The circumstance in which the two cases resemble may be capable of being shown to be the material circumstance; to be that on which all the consequences necessary to be taken into account in the particular discussion depend. In the example last given, the resemblance is one of relation; the fundamentum relationis being the management by a few persons of affairs in which a much greater number are interested along with them. Now, some may contend that this circumstance, which is com

§ I. THE word Analogy, as the name of a mode of reasoning, is generally taken for some kind of argument supposed to be of an inductive nature, but not amounting to a complete induction. There is no word, however, which is used more loosely, or in a greater variety of senses, than Analogy. It sometimes stands for arguments which may be examples of the most rigorous Induction. Arch-mon to the two cases, and the various bishop Whately, for instance, following Ferguson and other writers, defines Analogy conformably to its primitive acceptation, that which was given to it by mathematicians, Resemblance of Relations. In this sense, when a country which has sent out colonies is termed the mother

consequences which follow from it, have the chief share in determining all the effects which make up what we term good or bad administration. If they can establish this, their argument has the force of a rigorous induction; if they cannot, they are said to have failed in proving the

analogy between the two cases; a mode of speech which implies that when the analogy can be proved, the argument founded on it cannot be resisted.

the properties of A which is the cause of m, or united with it by any law. After rejecting all which we know to have nothing to do with it, there remain several between which we are unable to decide: of which remaining properties B possesses one or more. This accordingly we consider as affording grounds, of more or less strength, for concluding by analogy that B possesses the attribute m.

known to be connected with m; they must not be properties known to be unconnected with it. If, either by processes of elimination, or by deduction from previous knowledge of the laws of the properties in question, it § 2. It is on the whole more usual, can be concluded that they have nohowever, to extend the name of ana- thing to do with m, the argument of logical evidence to arguments from analogy is put out of court. The any sort of resemblance, provided supposition must be that m is an they do not amount to a complete effect really dependent on some proinduction without peculiarly dis-perty of A, but we know not on tinguishing resemblance of relations. which. We cannot point out any of Analogical reasoning, in this sense, may be reduced to the following formula:-Two things resemble each other in one or more respects; a certain proposition is true of the one, therefore it true of the other. But we have nothing here by which to discriminate analogy from induction, since this type will serve for all reasoning from experience. In the strictest induction, equally with the faintest analogy, we conclude because A resembles B in one or more properties, that it does so in a certain other property. The difference is, that in the case of a complete induction it has been previously shown, by due comparison of instances, that there is an invariable conjunction between the former property or properties and the latter property; but in what is called analogical reasoning, no such conjunction has been made out. There have been no opportunities of putting in practice the Method of Difference, or even the Method of Agreement; but we conclude (and that is all which the argu-perties dependent on that ultimate ment of analogy amounts to) that a fact m, known to be true of A, is more likely to be true of B if B agrees with A in some of its properties, (even though no connection is known to exist between m and those properties,) than if no resemblance at all could be traced between B and any other thing known to possess the attribute m.

To this argument it is of course requisite that the properties common to A with B shall be merely not

There can be no doubt that every such resemblance which can be pointed out between B and A affords some degree of probability, beyond what would otherwise exist, in favour of the conclusion drawn from it. If B resembled A in all its ultimate properties, its possessing the attribute m would be a certainty, not a probability; and every resemblance which can be shown to exist between them places it by so much the nearer to that point. If the resemblance be in an ultimate property, there will be resemblance in all the derivative pro

property, and of these m may be one. If the resemblance be in a derivative property, there is reason to expect resemblance in the ultimate property on which it depends, and in the other derivative properties dependent on the same ultimate property. Every resemblance which can be shown to exist affords ground for expecting an indefinite number of other resemblances: the particular resemblance sought will, therefore, be oftener found among things thus known to

resemble, than among things between | unknown will on the average of which we know of no resemblance. cases bear some proportion to those For example, I might infer that which are known. There will, therethere are probably inhabitants in the fore, be a competition between the moon, because there are inhabitants known points of agreement and the on the earth, in the sea, and in the known points of difference in A and air; and this is the evidence of ana- B; and according as the one or the logy. The circumstance of having other may be deemed to preponde. inhabitants is here assumed not to rate, the probability derived from be an ultimate property, but (as is analogy will be for or against B's reasonable to suppose) a consequence having the property m. The moon, of other properties; and depending, for instance, agrees with the earth in therefore, in the case of the earth, on the circumstances already mentioned; some of its properties as a portion of but differs in being smaller, in having the universe, but on which of those its surface more unequal, and approperties we know not. Now the parently volcanic throughout, in havmoon resembles the earth in being aling, at least on the side next the solid, opaque, nearly spherical sub-earth, no atmosphere sufficient to restance, appearing to contain, or to fract light, no clouds, and (it is therehave contained, active volcanoes; re- fore concluded) no water. These ceiving heat and light from the sun differences, considered merely as in about the same quantity as our such, might perhaps balance the reearth; revolving on its axis; com- semblances, so that analogy would posed of materials which gravitate, afford no presumption either way. and obeying all the various laws re- But considering that some of the sulting from that property. And I circumstances which are wanting on think no one will deny that if this the moon are among those which, on were all that was known of the moon, the earth, are found to be indispensthe existence of inhabitants in that able conditions of animal life, we may luminary would derive from these conclude that if that phenomenon various resemblances to the earth a does exist in the moon, (or at all greater degree of probability than it events on the nearer side,) it must be would otherwise have: though the as an effect of causes totally different amount of the augmentation it would from those on which it depends here; be useless to attempt to estimate. as a consequence, therefore, of the moon's differences from the earth, not of the points of agreement. Viewed in this light, all the resemblances which exist become presumptions against, not in favour of, the moon's being inhabited. Since life cannot exist there in the manner in which it exists here, the greater the resemblance of the lunar world to the terrestrial in other respects, the less reason we have to believe that it can contain life.

If, however, every resemblance proved between B and A, in any point not known to be immaterial with respect to m, forms some additional reason for presuming that B has the attribute m, it is clear, è contra, that every dissimilarity which can be proved between them furnishes a counter-probability of the same nature on the other side. It is not indeed unusual that different ultimate properties should, in some particular instances, produce the same derivative property; but on the whole it is certain that things which differ in their ultimate properties will differ at least as much in the aggregate of their derivative properties, and that the differences which are

There are, however, other bodies in our system, between which and the earth there is a much closer resemblance, which possess an atmosphere, clouds, consequently water, (or some fluid analogous to it,) and even give strong indications of snow in their

polar regions; while the cold or heat, without any antecedent evidence of though differing greatly on the aver- a connection between them, depends age from ours, is, in some parts at on the extent of ascertained releast of those planets, possibly not semblance, compared first with the more extreme than in some regions amount of ascertained difference, and of our own which are habitable. To next with the extent of the unexbalance these agreements, the ascer-plored region of unascertained protained differences are chiefly in the perties; it follows that where the average light and heat, velocity of resemblance is very great, the ascerrotation, density of material, inten- tained difference very small, and our sity of gravity, and similar circum- knowledge of the subject-matter tolerstances of a secondary kind. With ably extensive, the argument from regard to these planets, therefore, the analogy may approach in strength argument of analogy gives a decided very near to a valid induction. If, preponderance in favour of their re- after much observation of B, we find sembling the earth in any of its de- that it agrees with A in nine out of rivative properties, such as that of ten of its known properties, we may having inhabitants; though, when we conclude with a probability of nine consider how immeasurably multitu- to one, that it will possess any given dinous are those of their properties derivative property of A. If we diswhich we are entirely ignorant of, cover, for example, an unknown anicompared with the few which we mal or plant, resembling closely some know, we can attach but trifling known one in the greater number of weight to any considerations of re- the properties we observe in it, but semblance in which the known ele- differing in some few, we may reasonments bear so inconsiderable a pro-ably expect to find in the unobserved portion to the unknown.

Besides the competition between analogy and diversity, there may be a competition of conflicting analogies. The new case may be similar in some of its circumstances to cases in which the fact m exists, but in others to cases in which it is known not to exist. Amber has some properties in common with vegetable, others with mineral products. A painting of unknown origin may resemble, in certain of its characters, known works of a particular master, but in others it may as strikingly resemble those of some other painter. A vase may bear some analogy to works of Grecian, and some to those of Etruscan or Egyptian art. We are of course supposing that it does not possess any quality which has been ascertained, by a sufficient induction, to be a conclusive mark either of the one or of the other.

remainder of its properties a general agreement with those of the former, but also a difference corresponding proportionately to the amount of observed diversity.

It thus appears that the conclusions derived from analogy are only of any considerable value when the case to which we reason is an adjacent case; adjacent, not as before, in place or. time, but in circumstances. In the case of effects of which the causes are imperfectly or not at all known, when consequently the observed order of their occurrence amounts only to an empirical law, it often happens that the conditions which have co-existed whenever the effect was observed have been very numerous. Now if a new case presents itself, in which all these conditions do not exist, but the far greater part of them do, some one or a few only being wanting, the inference that the effect will occur, notwithstanding this deficiency of com§ 3. Since the value of an ana-plete resemblance to the cases in logical argument inferring one re- which it has been observed, may, semblance from other resemblances though of the nature of analogy, pos